Algebraic Properties

Question 1

Associative Properties of Addition and Multiplication

Answer 1

The manner by which numbers are grouped together for addition or multiplication does not affect the sum or product.

These two properties are independent of each other and only apply to their respective operations. (3x7)+10 != 3(7+10)

Question 2

Sum

Answer 2

The solution to an addition problem.

Question 3

Product

Answer 3

The solution to a multiplication problem.

Question 4

Quotient

Answer 4

The solution to a division problem.

Question 5

Difference

Answer 5

The solution to a subtraction problem.

Question 6

The Commutative Property of Multiplication

Answer 6

Re-ordering a set of real numbers multiplied together will not affect the product.

Question 7

Identity Property of Addition

Answer 7

Adding 0 to any real number will not change the value of that number.

Question 8

Identity Property of Multiplication

Answer 8

Multiplying any real number by 1 will not change the value of that number.

Question 9

Symmetric Property

Answer 9

Two equal quantities remain equal even if written on opposite sides of an equal sign.

5 = x = 5

Question 10

Distributive Property of Multiplication

Answer 10

If a, b, and c are real numbers, then a(b+c) = ab+ac

Question 11

Additive Inverse Property

Answer 11

Adding any real number to its opposite will result in 0, the additive identity.

-a+a=0

Question 12

Multiplicative Inverse Property

Answer 12

Multiplying a number by its reciprocal results in 1, the multiplicative identity.

(a/b)(b/a) = ab/ab = 1

Question 13

Transitive Property

Answer 13

If a=b and b=c the a=c.